Question

quiz 6
20 points possible answered: 10/20
question 11
if the hypotenuse of a right triangle is 6 and one leg is 5, what is the length of the other leg?

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Let the unknown leg be \(x\), we know \(c = 6\), one leg \(a=5\), so we have \(5^{2}+x^{2}=6^{2}\).

Step2: Solve for \(x\)

First, calculate \(5^{2}=25\) and \(6^{2}=36\). Then the equation becomes \(25 + x^{2}=36\). Subtract 25 from both sides: \(x^{2}=36 - 25=11\). Take the square root of both sides: \(x=\sqrt{11}\) (we take the positive root since length can't be negative).

Answer:

\(\sqrt{11}\)